GATE CS 2024 Set 2 — Question 35
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Algorithms → Dynamic Programming → Longest Increasing Subsequence
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Question
Let be an array containing integer values. The distance of is defined as the minimum number of elements in that must be replaced with another integer so that the resulting array is sorted in non-decreasing order. The distance of the array is ___________
Correct answer
3 to 3
Solution
To minimize the number of replacements required to make the array sorted in non-decreasing order, we should keep the maximum number of elements from the original array that already form a non-decreasing subsequence. The remaining elements will be replaced.Let be the length of the array. The minimum number of replacements is given by:The given array is . The length .Let's find the Longest Non-Decreasing Subsequence:
1.Start with the first element:
2.Next is 5 ():
3.Next is 3. It breaks the order with 5. We can form (replacing 5 in the active list of potential end values).
4.Next is 1. It breaks the order with 2. We can form .
5.Next is 4 ():
6.Next is 2. It breaks the order with 3. We can form .
7.Next is 6 ():
The length of the LNDS is 4. One such subsequence is (indices 0, 2, 4, 6).Therefore, the minimum number of replacements is:Continue learning with Success Tracker
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